Although there are exceptions I guess, our genset is one that cranks off the chassis batteries. If that’s your instance, than the fridge issue is a separate one probably related to its circuitry, such as the board. The genset’s clicking implies battery or cable connection problems.
It’s not uncommon to read herein of poor + or ground connections at the genset or one of its switches. If your coach starts okay, and someone here can verify your 2002 Marquis genset is chassis battery dependent, then the first place I’d check is those genset connections. There should be one extra heavy black cable going to a chassis bat. Positive post if the genset starts from them.
Hopefully this gives you some minimal guidance at least.
Joel